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arXiv:2112.04435 · PRX Quantum

Simulating the Electronic Structure of Spin Defects on Quantum Computers

Benchen Huang, Marco Govoni, Giulia Galli

Published Mar 10, 2022• 41 citations
arXivHTMLPDF

Abstract

We present calculations of both the ground-and excited-state energies of spin defects in solids carried out on a quantum computer, using a hybrid classical-quantum protocol.We focus on the negatively charged nitrogen-vacancy center in diamond and on the double vacancy in 4H SiC, which are of interest for the realization of quantum technologies.We employ a recently developed first-principles quantum embedding theory to describe point defects embedded in a periodic crystal and to derive an effective Hamiltonian, which is then transformed to a qubit Hamiltonian by means of a parity transformation.We use the variational quantum eigensolver (VQE) and quantum subspace expansion methods to obtain the ground and excited states of spin qubits, respectively, and we propose a promising strategy for noise mitigation.We show that by combining zero-noise extrapolation techniques and constraints on electron occupation to overcome the unphysical-state problem of the VQE algorithm, one can obtain reasonably accurate results on near-term-noisy architectures for ground-and excited-state properties of spin defects.

DOI
10.1103/prxquantum.3.010339

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We present calculations of both the ground-and excited-state energies of spin defects in solids carried out on a quantum computer, using a hybrid classical-quantum protocol.We focus on the negatively charged nitrogen-vacancy center in diamond and on the double vacancy in 4H SiC, which are of interest for the realization of quantum technologies.We employ a recently developed first-principles quantum embedding theory to describe point defects embedded in a periodic crystal and to derive an effective Hamiltonian, which is then transformed to a qubit Hamiltonian by means of a parity transformation.We use the variational quantum eigensolver (VQE) and quantum subspace expansion methods to obtain the ground and excited states of spin qubits, respectively, and we propose a promising strategy for noise mitigation.We show that by combining zero-noise extrapolation techniques and constraints on electron occupation to overcome the unphysical-state problem of the VQE algorithm, one can obtain reasonably accurate results on near-term-noisy architectures for ground-and excited-state properties of spin defects.
Certain point defects in solids can efficiently be used as qubits for applications in quantum technology. They have spin states that are initializable, readable, robust, and can be manipulated optically. New theoretical methods are needed to find the best host materials and defect configurations. Most methods proposed so far rely either on cluster models or restrict the many-body treatment of the defects to a subspace of single-particle orbitals. We explore best practices and theory for the use of quantum Monte Carlo to predict the excitation spectra for spin defects, by using the negatively charged nitrogen vacancy (${\mathrm{NV}}^{\ensuremath{-}}$) center in diamond as a test system. Quantum Monte Carlo can be used to explicitly simulate electronic correlations with larger systems and sets of orbitals than previous methods due to favorable scaling with respect to system size and computing power. We consider different trial wave functions for variational and diffusion Monte Carlo methods, explore the nodal surface errors of the ground and excited state wave functions, and study whether the variational principle holds for the excited states. We compute the vertical excitation energies in different simulation cell sizes and extrapolate to infinite system size, and include backflow corrections to the extrapolated energies. The final results for vertical excitation energies are found to overestimate the experimental estimates, but the triplet-to-triplet and singlet-to-singlet transitions are accurate against experiment. Finally, we list further developments for QMC needed to address the problem of accurately predicting structural and spin properties of the solid-state defects.
We propose a computational protocol for quantum simulations of fermionic Hamiltonians on a quantum computer, enabling calculations on spin defect systems which were previously not feasible using conventional encodings and a unitary coupled-cluster ansatz of variational quantum eigensolvers. We combine a qubit-efficient encoding scheme mapping Slater determinants onto qubits with a modified qubit-coupled cluster ansatz and noise-mitigation techniques. Our strategy leads to a substantial improvement in the scaling of circuit gate counts and in the number of required qubits, and to a decrease in the number of required variational parameters, thus increasing the resilience to noise. We present results for spin defects of interest for quantum technologies, going beyond minimum models for the negatively charged nitrogen vacancy center in diamonds and the double vacancy in 4H silicon carbide (4H-SiC) and tackling a defect as complex as negatively charged silicon vacancy in 4H-SiC for the first time.
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Nitrogen-vacancy (NV) complex in diamond is one of the most prominent solid state defects as the negatively charged NV defect (NV−) is a leading contender for quantum technologies. In quantum information processing applications, NV− is photoexcited that often leads to photoionization to neutral NV defect, NV0, and re-ionization back to NV− should occur to control the S=1 spin of NV−. As a consequence, understanding the photophysics of NV0 is crucial for controlling NV−. Furthermore, recent studies have shown that the S=1/2 electron spin of NV0 can also be initialized and read out at certain conditions that turns single NV0 a potential quantum bit. Quantum optics protocols rest on detailed knowledge on the electronic structure of the given system, which is obviously missing for NV0 in diamond. In this study, we combine the group theory and density functional theory calculations toward exploring the nature of the ground and excited states of NV0. We show that the effective three-electron system of NV0 leads to high correlation effects that make this system very challenging for ab initio simulations.
Quantum computers hold promise to greatly improve the efficiency of quantum simulations of materials and to enable the investigation of systems and properties more complex than tractable on classical architectures. Here, we discuss computational frameworks to carry out electronic structure calculations of solids on noisy intermediate scale quantum computers using embedding theories and effective many-body Hamiltonians. We focus on a specific class of materials, i.e., spin defects in solids, which are promising systems to build future quantum technologies, e.g., computers, sensors and devices for quantum communications. Although quantum simulations on quantum architectures are in their infancy, promising results for realistic systems appear within reach.
A quantitative description of the excited electronic states of point defects and impurities is crucial for understanding materials properties, and possible applications of defects in quantum technologies. This is a considerable challenge for computational methods, since Kohn-Sham density functional theory (DFT) is inherently a ground-state theory, while higher-level methods are often too computationally expensive for defect systems. Recently, embedding approaches have been applied that treat defect states with many-body methods, while using DFT to describe the bulk host material. We implement such an embedding method, based on Wannierization of defect orbitals and the constrained random-phase approximation approach, and perform systematic characterization of the method for three distinct systems with current technological relevance: a carbon dimer replacing a B and N pair in bulk hexagonal BN (CBCN{\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}CB​CN​), the negatively charged nitrogen-vacancy center in diamond (${\mathrm{NV}}^{\ensuremath{-}}$), and an Fe impurity on the Al site in wurtzite AlN (FeAl{\text{Fe}}_{\text{Al}}FeAl​). In the context of these test-case defects, we demonstrate that crucial considerations of the methodology include convergence of the bulk screening of the active-space Coulomb interaction, the choice of exchange-correlation functional for the initial DFT calculation, and the treatment of the ``double-counting'' correction. For CBCN{\mathrm{C}}_{\text{B}}{\mathrm{C}}_{\text{N}}CB​CN​ we show that the embedding approach gives many-body states in agreement with analytical results on the Hubbard dimer model, which allows us to elucidate the effects of the DFT functional and double-counting correction. For the ${\mathrm{NV}}^{\ensuremath{-}}$ center, our method demonstrates good quantitative agreement with experiments for the zero-phonon line of the triplet-triplet transition. Finally, we illustrate challenges associated with this method for determining the energies and orderings of the complex spin multiplets in FeAl{\text{Fe}}_{\text{Al}}FeAl​.